Even assuming an extremely virulent and global zombie infection, I suspect that electricity might still continue running for weeks if not months, at least in some places. But the transportation and and fuel delivery infrastructure that supports our electrical grid would rapidly begin to breakdown, even in areas the infection has not yet reached. Everything is so interdependent that things would go south very quickly. I'd remain cautiously optimistic that resources and labor expectations would give priority to basic services like power, water, communications and essential government services. But eventually, utility workers will become afraid to leave their homes, want to focus on their own preps and/or lack the fuel to drive themselves to work. Once that begins to happen, I imagine what we've come to recognize as a functioning society would rapidly grind to a halt.
I'm going to do my damndest to find an article (written by a power plant employee) that explains how long modern electrical plants would last in a major disaster. I ran across it once and should have copied it somewhere. The answer is they will all go offline shockingly fast, like in a matter of hours, not days. Electrical plants depend on 'just on time' delivery of fuel and other supplies that make them (ironically) very dependent on the very grid they provide.
I'll post it if I find it.
And... found it (or something pretty damn close). Linky: http://www.straightdope.com/columns/read/2165/when-the-zombies-take-over-how-long-till-the-electricity-fails
Summary for the tl;dr crowd:Bottom line? My guess is that within 4-6 hours there would be scattered blackouts and brownouts in numerous areas, within 12 hours much of the system would be unstable, and within 24 hours most portions of the United States and Canada, aside from a rare island of service in a rural area near a hydroelectric source, would be without power. Some installations served by wind farms and solar might continue, but they would be very small. By the end of a week, I'd be surprised if more than a few abandoned sites were still supplying power.